\clearpage
\item \subquestionpoints{5}
Derive an expression for the mean of the distribution. Show that
$\mathbb{E}[Y\mid X;\theta]$ can be represented as the gradient of the
log-partition function $a$ with respect to the natural parameter $\eta$.

\textbf{Hint:} Start with observing that $\frac{\partial}{\partial \eta} \int
p(y;\eta) dy = \int \frac{\partial}{\partial \eta} p(y;\eta) dy$.

\ifnum\solutions=1{
  \input{04-glm-convexity/01-mean-sol}
}\fi
